if a cylinder 5cm diameter and 12cm high is on a train, how fast does train need to deceletate to tip it over

Question

the cup is filled with water and it cannot slide just tip over

Answer 1

So is it a cup or a cylinder?

The center of mass of the cylinder is at (2.5. 6).
The cylinder will tip over when the center of mass has moved over the pivoting point. That will hap pend when angle A is increased beyond this relationship

tan(A)= r/(0.5h)=2.5/6

also

tan(A) = F/W
F- force exerted by deceleration
W- weight of the cylinder

F= ma
W=mg we have
tan(A) = ma/mg=2.5/6
a= g (2.5/6)=4.1 m/s^2